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1911 Encyclopædia Britannica/Leibnitz, Gottfried Wilhelm

LEIBNITZ (Leibniz), GOTTFRIED WILHELM (1646-1716), German philosopher, mathematician and man of affairs, was born on the 1st of July 1646 at Leipzig, where his father was professor of moral philosophy. Though the name Leibniz, Leibnitz or Lubeniecz was originally Slavonic, his ancestors were German, and for three generations had been in the employment of the Saxon government. Young Leibnitz was sent to the Nicolai school at Leipzig, but, from 1652 when his father died, seems to have been for the most part his own teacher. From his father he had acquired a love of historical study. The German books at his command were soon read through, and with the help of two Latin books-the Thesaurus Chronologicus of Calvisius and an illustrated edition of Livy-he learned Latin at the age of eight. His father's library was now thrown open to him, to his great joy, with the permission, “ Tolle, lege.” Before he was twelve he could read Latin easily and had begun Greek; he had also remarkable facility in writing Latin verse. He next turned to the study of logic, attempting already to reform its doctrines, and zealously reading the scholastic and some of the Protestant theologians.

At the age of fifteen, he entered the university of Leipzig as a law student, His first two years were devoted to philosophy under Jakob Thomasius, a Neo-Aristotelian, who is looked upon as having founded the scientific study of the history of philosophy in Germany. It was at this time probably that he first made acquaintance with the modern thinkers who had already revolutionized science and philosophy, Francis Bacon, Cardayn and Campanella, Kepler, Galileo and Descartes; and he began to consider the difference between the old and new ways of regarding nature. He resolved to study mathematics. It was not, however, till the summer of 1663, which he spent at Iena under E. Weigel, that he obtained the instructions of a mathematician of repute; nor was the deeper study of mathematics entered upon till his visit to Paris and acquaintance with Huygens many years later.

The next three years he devoted to legal studies, and in 1666 applied for the degree of doctor of law, with a view to obtaining the post of assessor. Being refused on the ground of his youth he left his native town for ever. The doctor's degree refused him there was at once (November 5, 1666) conferred on him at Altdorf-the university town of the free city of Nuremberg where his brilliant dissertation procured him the immediate offer of a professor's chair. This, however, he declined, having, as he said, “very different things in view.” Leibnitz, not yet twenty-one years of age, was already the author of several remarkable essays. In his bachelor's dissertation De principio indifvidui (1663), he defended the nominalistic doctrine that individuality is constituted by the whole entity or essence of a thing; his arithmetical tract De complexionibus, published in an extended form under the title De arte combinatorial (1666), is an essay towards his life-long project of a reformed symbolism and method of thought; and besides these there are our juridical essays, including the N ova methodus docendi discendiqzte juris, written in the intervals of his journey from Leipzig to Altdorf. This last essay is remarkable, not only for the reconstruction it attempted of the Corpus Juris, but as containing the first clear recognition of the importance of the historical method in law. Nuremberg was a centre of the Rosicrucians, and Leibnitz, busying himself with writings of the alchemists, soon gained such a knowledge of their tenets that he was supposed to be one of the secret brotherhood, and was even elected their secretary. A more important result of his visit to Nuremberg was his acquaintance with Iohann Christian von Boyneburg (1622-1672), formerly first minister to the elector of Mainz, and one of the most distinguished German statesmen of the day. By his advice Leibnitz printed his Nuw methodus in 1667, dedicated it to the elector, and, going to Mainz, presented it to him in person. It was thus that Leibnitz entered the service of the elector of Mainz, at first as an assistant in the revision of the statute-book, afterwards on more important work.

The policy of the elector, which the pen of Leibnitz was now called upon to promote, was to maintain the security of the German empire, threatened on the west by the aggressive power of France, on the east by Turkey and Russia. Thus when in 1669 the crown of Poland became vacant, it fell to Leibnitz to support the claims of the German candidate, which he did in his first political writing, Specimen demonstration um potiticarum pro rege Pulonorum etigendo, attempting, under the guise of a Catholic Polish nobleman, to show by mathematical demonstration that it was necessary in the interest of Poland that it should have the count palatine of Neuburg as its king. But neither the diplomatic skill of Boyneburg, who had been sent as plenipotentiary to the election at Warsaw, nor the arguments of Leibnitz were successful, and a Polish prince was elected to fill the vacant throne.

A greater danger threatened Germany in the aggressions of Louis XIV. (see France: History). Though Holland was in most immediate danger, the seizure of Lorraine in 1670 showed that Germany too was threatened. It was in this year that Leibnitz wrote his Thoughts on Public Safety)[1] in which he urged the formation of a new “Rheinbund” for the protection of Germany, and contended that the states of Europe should employ their power, not against one another, but in the conquest of the non-Christian world, in which Egypt, “one of the best situated lands in the world,” would fall to France. The plan thus proposed of averting the threatened attack on Germany by a French expedition to Egypt was discussed with Boyneburg, and obtained the approval of the elector. French relations with Turkey were at the time so strained as to make a breach imminent, and at the close of 1671, about the time when the war with Holland broke out, Louis himself was approached by a letter from Boyneburg and a short memorial from the pen of Leibnitz, who attempted to show that Holland itself, as a mercantile power trading with the East, might be best attacked through Egypt, while nothing would be easier for France or would more largely increase her power than the conquest of Egypt. On February 12, 1672, a request came from the French secretary of state, Simon Arnauld de Pomponne (1618-1699), that Leibnitz should go to Paris. Louis seems still to have kept the matter in view, but never granted Leibnitz the personal interview he desired, while Pomponne wrote, “I have nothing against the plan of a holy war, but such plans, you know, since the days of St Louis, have ceased to be the fashion.” Not yet discouraged, Leibnitz wrote a full account of his project for the king,[2] and a summary of the same[3] evidently intended for Boyneburg. But Boyneburg died in December 1672, before the latter could be sent to him. Nor did the former ever reach its destination. The French quarrel with the Porte was made up, and the plan of a French expedition to Egypt disappeared from practical politics till the time of Napoleon. The history of this scheme, and the reason of Leibnitz's journey to Paris, long remained hidden in the archives of the Hanoverian library. It was on his taking possession of Hanover in 1803 that Napoleon learned, through the Consitium Aegyptiacum, that the idea of a French conquest of Egypt had been first put forward by a German philosopher. In the same year there was published in London an account of the Justa dissertatio[4] of which the British Government had procured a copy in 1799. But it was only with the appearance of the edition of Leibnitz's works begun by Onno Klopp in 1864 that the full history of the scheme was made known.

Leibnitz had other than political ends in view in his visit to France. It was as the centre of literature and science that Paris chiefly attracted him. Political duties never made him lose sight of his philosophical and scientific interests. At Mainz he was still busied with the question of the 'relation between the old and new methods in philosophy. In a letter to Jakob Thomasius (1669) he contends that the mechanical explanation of nature by magnitude, figure and motion alone is not inconsistent with the doctrines of Aristotle's Physics, in which he finds more truth than in the Meditations of Descartes. Yet these qualities of bodies, he argues in 1668 (in an essay published without his knowledge under the title Confessio naturae contra atheistas), require an incorporeal principle, or God, for their ultimate explanation. He also wrote at this time a defence of the doctrine of the Trinity against Wissowatius (1669), and an essay on philosophic style, introductory to an edition of the Antibarbarus of Nizolius (1670). Clearness and distinctness alone, he says, are what makes a philosophic style, and no language is better suited for this popular exposition than the German. In 1671 he issued a Hypothesis physica nova, in which, agreeing with Descartes that corporeal phenomena should be explained from motion, he carried out the mechanical explanation of nature by contending that the original of this motion is a fine aether, similar to light, or rather constituting it, which, penetrating all bodies in the direction of the earth's axis, produces the phenomena of gravity, elasticity, &c. The first part of the essay, on concrete motion, was dedicated to the Royal Society of London, the second, on abstract motion, to the French Academy.

At Paris Leibnitz met with Arnauld, Malebranche and, more important still, with Christian Huygens. This was pre-eminently the period of his mathematical and physical activity. Before leaving Mainz he was able to announce[5] an imposing list of discoveries, and plans for discoveries, arrived at by means of his new logical art, in natural philosophy, mathematics, mechanics, optics, hydrostatics, pneumatics and nautical science, not to speak of new ideas in law, theology and politics. Chief among these discoveries was that of a calculating machine for performing more complicated operations than that of Pascal-multiplying, dividing and extracting roots, as Well as adding and subtracting. This machine was exhibited to the Academy of Paris and to the Royal Society of London, and Leibnitz was elected a fellow of the latter society in April 1673.[6] In January of this year he had gone to London as an attaché on a political mission from the elector of Mainz, returning in March to Paris, and while in London had become personally acquainted with Oldenburg, the secretary of the Royal Society, with whom he had already corresponded, with Boyle the chemist and Pell the mathematician. It is from this period that we must date ~the impulse that directed him anew to mathematics. By Pell he had been referred to Mercator's Logarithmotechmica as already containing some numerical observations which Leibnitz had thought original on his own part; and, on his return to Paris, he devoted himself to the study of higher geometry under Huygens, entering almost at once upon the series of investigations which culminated in his discovery of the differential and integral calculus (see Infinitesimal Calculus).

Shortly after his return to Paris in 1673, Leibnitz ceased to be in the Mainz service any more than in name, but in the same year entered the employment of Duke John Frederick of Brunswick-Lüneburg, with whom he had corresponded for some time.

In 1676 he removed at the duke's request to Hanover, travelling thither by way of London and Amsterdam. At Amsterdam he saw and conversed with Spinoza, and carried away with him extracts from the latter's unpublished Ethica.

For the next forty years, and under three successive princes, Leibnitz was in the service of the Brunswick family, and his headquarters were at Hanover, where he had charge of the ducal library. Leibnitz thus passed into a political atmosphere formed by the dynastic aims of the typical German state (see Hanover; Brunswick). He supported the claim of Hanover to appoint an ambassador at the congress of Nimeguen (1676)[7] to defend the establishment of primogeniture in the Lüneburg branch of the Brunswick family; and, when the proposal was made to raise the duke of Hanover to the electorate, he had to show that this did not interfere with the rights of the duke of Wtirttemberg. In 1692 the duke of Hanover was made elector. Before, and with a view to this, Leibnitz had been employed by him to write the history of the Brunswick-Lüneburg family, and, to collect material for his history, had undertaken a journey through Germany and Italy in 1687-1690, visiting and examining the records in Marburg, Frankfort-on-the-Main, Munich, Vienna (where he remained nine months), Venice, Modena and Rome. At Rome he was offered the custodianship of the Vatican library on condition of his, joining the Catholic Church.

About this time, too, his thoughts and energies were partly taken up with the scheme for the reunion of the Catholic and Protestant Churches. At Mainz he had joined in an attempt made by the elector and Boyneburg to bring about a reconciliation, and now, chiefly through the energy and skill of the Catholic Royas de Spinola, and from the spirit of moderation which prevailed among the theologians he met with at Hanover in 1683, it almost seemed as if some agreement might be arrived at. In 1686 Leibnitz wrote his Systema theologirum[8] in which he strove to find common ground for Protestants and Catholics in the details of their creeds. But the English revolution of 1688 interfered with the scheme in Hanover, and it was soon found that the religious difficulties were greater than had at one time appeared. In the letters to Leibnitz from Bossuet, the land grave of Hessen-Rheinfels, and Madame de Brinon, the aim is obviously to make converts to Catholicism, not to arrive at a compromise with Protestantism, and when it was found that Leibnitz refused to be converted the correspondence ceased. A further scheme of church union in which Leibnitz was engaged, that between the Reformed and Lutheran Churches, met with no better success.

Returning from Italy in 169O, Leibnitz was appointed librarian at Wolfenbiittel by Duke Anton of Brunswick-Wolfenbiittel. Some years afterwards began his connexion with Berlin through his friendship with the electress Sophie Charlotte of Brandenburg and her mother the princess Sophie of Hanover. He was invited to Berlin in 1700, and on the 11th Tuly of that year the academy (Akademie der Wissenschaften) he had planned was founded, with himself as its president for life. In the same year he was made a privy councillor of justice by the elector of Brandenburg. Four years before he had received a like honour from the elector of Hanover, and twelve years afterwards the same distinction was conferred upon him by Peter the Great, to whom he gave a plan for an academy at St Petersburg, carried out after the czar's death. After the death of his royal pupil in 1705 his visits to Berlin became less frequent and less welcome, and in 1711 he was there for the last time. In the following year he undertook his fifth and last journey to Vienna, where he stayed till 1714. An attempt to found an academy of science there was defeated by the opposition of the Jesuits, but he now attained the honour he had coveted of an imperial privy councillor ship (1712), and, either at this time or on a previous occasion (1709), was made a baron of the empire (Reichsfreiherr). Leibnitz returned to Hanover in September 1714, but found the elector George Louis had already gone to assume the crown of England. Leibnitz would gladly have followed him to London, but was bidden to remain at Hanover and finish his history of Brunswick.

During the last thirty years Leibnitz had been busy with many matters. Mathematics, natural science,[9] philosophy, theology, history jurisprudence, politics (particularly the French wars with Germany, and the question of the Spanish succession), economics and philology, all gained a share of his attention; almost all of them he enriched with original observations.

His genealogical researches in Italy—through which he established the common origin of the families of Brunswick and Este-were not only preceded by an immense collection of historical sources, but enabled him to publish materials for a code of international law.[10] The history of Brunswick itself was the last work of his life, and had covered the period from 768 to 1005 when death ended his labours. But the government, in whose service and at whose order the work had been carried out, left it in the archives of the Hanover library till it was published by Pertz in 1843.

It was in the years between 1690 and 1716 that Leibnitz's chief philosophical works were composed, and during the first ten of these years the accounts of his system were, for the most part, preliminary sketches. Indeed, he never gave a full and systematic account of his doctrines. His views have to be gathered from letters to friends, from occasional articles in the Arla Erudifarum, the Journal des Szwauis, and other journals, and from one or two more extensive works. It is evident, however, that philosophy had not been entirely neglected in the years in which his pen was almost solely occupied with other matters. A letter to the duke of Brunswick, and another to Arnauld, in 1671, show that he had already reached his new notion of substance; but it is in the correspondence with Antoine Arnauld, between 1686 and 1690, that his fundamental ideas and the reasons for them are for the first time made clear. The appearance of Locke's Essay in 1690 induced him (1696) to note down his objections to it, and his own ideas on the same subjects. In 1703-1704 these were worked out in detail and ready for publication, when the death of the author whom they criticized prevented their appearance (first published by Raspe, 1765). In 1710 appeared the only complete and systematic philosophical work of his life-time, Esstzis de T héodicée sur la bonlé de Dieu, liz liberté de Fhommc, et Vorigine du mal, originally undertaken at the request of the late queen of Prussia, who had wished a reply to Bayle's opposition of faith and reason. In 1714 he wrote, for Prince Eugene of Savoy, a sketch of his system under the title of La lllonadologic, and in the same year appeared his Principe; de la nalurect de la grfice. The last few years of his life were perhaps more occupied with correspondence than any others, and, in a philosophical regard, were chiefly notable for the letters, which, through the desire of the new queen of England, he interchanged with Clarke, sur Dieu, Vtfme, Vespace, la dures. Leibnitz died on the 14th of November 1716, his closing years enfeebled by disease, harassed by controversy, embittered by neglect; but to the last he preserved the indomitable energy and power of work to which is largely due the position he holds as, more perhaps than any one in modern times, a man of almost universal attainments and almost universal genius. Neither at Berlin, in the academy which he had founded, nor in London, whither his sovereign had gone to rule, was any notice taken of his death. At Hanover, Eckhart, his secretary, was his only mourner; “ he was buried, ” says an eyewitness, “ more like a robber than what he really was, the ornament of his country.”[11] Only in the French Academy was the loss recognized, and a worthy eulogium devoted to his memory (November 13, 1717). The Qooth anniversary of his birth was celebrated in 1846, and in the same year were opened the Koniglichsiichsische Gesellschaft der Wissenschaften and the Kaiserliche Akademie der Wissenschaften in Leipzig and Vienna respectively. In 1883, a statue was erected to him at Leipzig.

Leibnitz possessed a wonderful power of rapid and continuous work. Even in travelling his time was employed in solving mathematical problems. He is described as moderate in his habits, quick of temper but easily appeased, charitable in his judgments of others, and tolerant of differences of opinion, though impatient of contradiction on small matters. He is also said to have been fond of money to the point of covetousness; he was certainly desirous of honour, and felt keenly the neglect in which his lust years were passed.

Philosophy—The central point in the philosophy of Leibnitz was only arrived at after many advances and corrections in his opinions. This point is his new doctrine of substance (p. 702),[12] and it is through it that unity is given to the succession of occasional writings, scattered over fifty years, in which he explained his views. More inclined to agree than to differ with what he read (p. 425), and borrowing from almost every philosophical system, his own standpoint is yet most closely related to that of Descartes, partly as consequence, partly by way of opposition. Cartesianism, Leibnitz often asserted, is the ante-room of truth, but the ante-room only. Descartes's separation of things into two heterogeneous substances only connected by the omnipotence of God, and the more logical absorption of both by Spinoza into. the one divine substance, followed from an erroneous conception of what the true nature of substance is. Substance, the ultimate reality, can only be conceived as force. Hence Leibnitz's metaphysical view of the monads as simple, percipient, self-active beings, the constituent elements of all things, his physical doctrines of the reality and constancy of force at the same time that space, matter and motion are merely phenomenal, and his psychological conception of the continuity and development of consciousness. In the closest connexion with the same stand his logical principles of consistency and sufficient reason, and the method he developed from them, his ethical end of perfection, and his crowning theological conception of the universe as the best possible world, and of God both as its efficient cause and its final harmony.

The ultimate elements of the universe are, according to Leibnitz, individual centres of force or monads. Why they should be individual, and not manifestations of one world-force, he never clearly proves.[13] His doctrine of individuality seems to have been arrived at, not by strict deduction from the nature of force, but rather from the empirical observation that it is by the manifestation of its activity that the separate existence of the individual becomes evident; for his system individuality is as fundamental as activity. “The monads," he says, “are the very atoms of nature —in a word, the elements of things,” but, as centres of force, they have neither parts, extension nor figure (p. 705). Hence their distinction from the atoms of Democritus and the materialists. They are metaphysical points or rather spiritual beings whose very nature it is to act. As the bent bow springs back to itself, so the monads naturally pass and are always assin into action without any aid but the absence of opposition (p. 122). Nor do they, like the atoms, act upon one another (p. 680); the action of each excludes that of every other. The activity of each is the result of its own past state, the determinator of its own future (pp. 706, 722). “The monads have no windows by which anything may go in or out" (p. 705).

Further, since all substances are of the nature of force, it follows that-“ in imitation of the notion which we have of souls "-they must contain something analogous to feeling and appetite. It is the nature of the monad to represent the many in one, and this is perception, by which external events are mirrored internally (p. 438). Through their own activity the monads mirror the universe (p. 725), but each in its own way and from its own point of view, that is, with a more or less perfect perception (p. 127); for the Cartesians were wrong in ignoring the infinite grades of perception, and identifying it with the refiex cognizance of it which may be called apperception. Every monad is thus a microcosm, the universe in little,[14] and according to the degree of its activity is the distinctness of its representation of the universe (p. 709). Thus Leibnitz, borrowing the Aristotelian term, calls the monads enlelechies, because they have a certain perfection (fb ér/1-e7és) and sufficiency (atmiprfra) which make them sources of their internal actions and, so to speak, incorporeal automata (p. 706). That the monads are not pure entelechies is shown by the differences amongst them. Excluding all external limitation, they are yet limited by their own nature. All created monads contain a passive element or matcria prima (pp. 440, 687, 725), in virtue of which their perceptions are more or less confused. As the activity of the monad consists in perception, this is inhibited by the passive principle, so that there arises in the monad an appetite or tendency to overcome the inhibition and become more perceptive, whence follows the change from one perception to another (pp. 706, 714). By the proportion of activity to passivity in it one monad is didcrentiated from another. The greater the amount of activity or of distinct perceptions the more perfect is the monad; the stronger the element of passivity, the more confused its perceptions, the less perfect is it (p. 709). The soul would be a divinity had it nothing but distinct perceptions (p. 520).

The monad is never without a perception; but, when it has a number of little perceptions with no means of distinction, a state similar to that of being stunned ensues, the monade nue being perpetually in this state (p. 707). Between this and the most distinct perception there is room for an infinite diversity of nature among the monads themselves. Thus no one monad is exactly the same as another; for, were it possible that there should be two identical, there would be no sufficient reason why God, who brings them into

actual existence, should put one of them at one definite time and place, the other at a different time and place. This is Leibnitz's principle of the identity of indiscemibles (pp. 277, 755); by it his early problem as to the principle of individuation is solved by the distinction between genus and individual being abolished, and every individual made sui generis. The principle thus established is formulated in Leibnitz's law of continuity, founded, he says, on the doctrine of the mathematical infinite, essential to geometry, and of importance in physics (pp. 104, 105), in accordance with which there is neither vacuum nor break in nature, but “everything takes place by degrees ” (p. 392), the different species of creatures rising f;y insensible steps from the lowest to the most perfect form (p. 312).

As in every monad each succeeding state is the consequence of the preceding, and as it is of the nature of every monad to mirror or represent the universe, it follows (p. 774) that the perceptive content of each monad is in “ accord ” or correspondence with that of every other (cf. p. 127), though this content is represented with infinitely varying degrees of perfection. This is Leibnitz's famous doctrine of pre-established harmony, in virtue of which the infinitely numerous independent substances of which the world is composed are related to each other and form one universe. It is essential to notice that it proceeds from the very nature of the monads as percipient, self-acting beings, and not from an arbitrary determination of the Deity.

From this harmony of self-determining percipient units Leibnitz has to explain the world of nature and mind. As everything that really exists is of the nature of spiritual or metaphysical points (p. 126), it follows that space and matter in the ordinary sense can only have a phenomenal existence (p. 745), being dependent not on the nature of the monads themselves but on the way in which they are perceived. Considering that'several thin s exist at the same time and in a certain order of coexistence, anti mistaking this constant relation for something that exists outside of them, the mind forms the confused perception of space (p. 768). But space and time are merely relative, the former an order of co existences, the latter of successions (pp. 682, 752). Hence not only the secondary qualities of Descartes and Locke, but their so-called primary qualities as well, are merely phenomenal (p. 445). The monads are really without position or distance from each other; but, as we perceive several simple substances, there is for us an aggre ate or extended mass. Body is thus active extension (pp. IIO, III . The unity of the aggregate depends entirely on our perceiving the monads composing it together. There is no such thing as an absolute vacuum or empty space, any more than there are indivisible material units or atoms from which all things are built up (pp. 126, 186, 277). Body, corporeal mass, or, as Leibnitz calls it, to distinguish it from the materia prima of which every monad partakes (p. 440), materia serunda, is thus only a “phenomenon bene fundatum " (p. 436). It is not a substantia but substantiae or subsstantiatum (p. 745). While this, however, is the only view consistent with Leibnitz's fundamental principles, and is often clearly stated by himself, he also speaks at other times of the matefia secunda as itself a composite substance, and of a real metaphysical bond between soul and ody. But these expressions occur chiefly in the letters to des Bosses, in which Leibnitz is trying to reconcile his views with the' doctrines of the Roman Catholic Church, especially with that of the real presence in the Eucharist, and are usually referred to by him as doctrines of faith or as hypothetical (see especially p. 680). The true vinculum subslarzlinle is not the materia secuiida, which a consistent development of Leibnitz's principles can only regard as phenomenal, but the materia prima, through which the monads are individualized and distinguished and their connexion rendered possible. And Leibnitz seems to recognize that the opposite assumption is inconsistent with his cardinal metaphysical view of the monads as the only realities.

From Leibnitz's doctrine of force as the ultimate reality it follows that his view of nature must be throughout dynamical. And though his project of a dynamic, or theory of natural philosophy, was never carried out, the outlines of his own theory and his criticism of the mechanical physics of Descartes are known to us. The whole distinction between the two lies in the difference between the mechanical and the dynamical views of nature. Descartes started from the reality of extension as constituting the nature of material substance, and found in magnitude, figure and motion the explanation of the material universe. Leibnitz, too, admitted the mechanical view of nature as giving the laws of corporeal phenomena (p. 438), applying also to everything that takes place in animal organisms,[15] even the human body (p. 777). But, as phenomenal, these laws must find their explanation in metaphysics, and thus in final causes (p. 155). All things, he says (in his Specimen Dynamicum), can be explained either by efficient or by final causes. ' But the latter method is not appropriate to individual occurrences,[16] though it must be applied when the laws of mechanism themselves need explanation (p. 678). For Dcscartcs's doctrine of the constancy of the quantity of motion (i.e. momentum) in the world Leibnitz substitutes the principle of the conservation of vis viva, and contends that the Cartesian position that motion is measured by velocity should be superseded by the law that moving force (vis matrix) is measured by the square of the velocity (pp. 192, 193>. The long controversy raised by this criticism was really caused by the ambiguity of the terms employed. The principles held by Descartes and Leibnitz were both correct, though different, and their conflict only apparent. Deseartcs's principle is now enunciated as the conservation of momentum, that of Leibnitz as the conservation of energy. Leibnitz further criticizes the Cartesian View that the mind can alter the direction of motion though it cannot initiate it, and contends that the quantity of “ vis directive, " estimated between the same parts, is constant (p. 108)a position developed in his statical theorem for determining geometrically the resultant of any number of forces acting at a point.

Like the monad, body, which is its analogue, has a passive and an active element. The former is the capacity of resistance, and includes impenetrability and inertia; the latter is active force (pp. 250, 687). Bodies, too, like the monads, are self»contained activities, receiving no impulse from Without-it is only by an accommodation to ordinary language that we speak of them as doing so-but moving themselves in harmony with each other (p. 250).

The psychology of Leibnitz is chiefly developed in the Nouveaux essais sur l’entendement humain, written in answer to Locke's famous Essay, and criticizing it chapter by chapter. In these essays he worked out a theory of the origin and development of knowledge in harmony with his metaphysical views, and thus without Locke's implied assumption of the mutual influence of soul and body. When one monad in an aggregate perceives the others so clearly that they are in comparison with it bare monads (monades nues), it is said to be the ruling monad of the aggregate, not because it actually does exert an influence over the rest, but because, being in closing correspondence with them, and yet having so much clearer perception, it seems to do so (p. 683). This monad is called the entelechy or soul of the aggregate or body, and as such mirrors the aggregate in the first place and the universe through it (p. 710). Each soul or entelechy is surrounded by an infinite number of monads forming its body (p. 714); soul and body together make a living being, and, as their laws are in perfect harmony-a harmony established between the whole realm of final causes and that of efficient causes (p. 714)-we have the same result as if one influenced the other. This is further explained by Leibnitz in his well-known illustration of the different ways in which two clocks may keep exactly the same time. The machinery of the one may actually move that of the other, or whenever one moves the mechanician may make a similar alteration in the other, or they may have been so perfectly constructed at first as to continue to correspond at every instant without any further influence (pp. 133, 134). The first way represents the common (Locke's) theory of mutual influence, the second the method of the occasionalists, the third that of pre-established harmony. Thus the body does not act on the soul in the production of cognition, nor the soul on the body in the production of motion. The body acts just as if it had no soul, the soul as if it had no body (p. 711). Instead, therefore, of all knowledge coming to us directly or indirectly through the bodily senses, it is all developed by the soul's own activity, and sensuous perception is itself but a confused kind of cognition. Not a certain select class of our ideas only (as Descartes held), but all our ideas, are innate, though only worked up into actual cognition in the development of knowledge (p. 212). To the aphorism made use of by Locke, “ Nihil est in intellect quod non prius fuerit in sensu, " must be added the clause, “ nisi intellect us ipse " (p. 223). The soul at birth is not comparable to a laibula ram, but rather to an unworked block of marble, the hidden veins of which already determine the form it is to assume in the hands of the sculptor (p. 196). Nor, again, can the soul ever be without perception; for it has no other nature than that of a percipient active being (p. 246). Apparently dreamless sleep is to be accounted for by unconscious perception (p. 223); and it is by such insensible perceptions that Leibnitz explains his doctrine of pre-established harmony (p. 197).

In the human soul perception is developed into thought, and there is thus an infinite though gradual difference between it and the mere monad (p. 464). As all knowledge is implicit in the soul, it follows that its perfection depends on the efficiency of the instrument by which it is developed. Hence the importance, in Leibnitz's system, of the logical principles and method, the consideration of which occupied him at intervals throughout his whole career.

There are two kinds of truths-(1) truths of reasoning, and (2) truths of fact (pp. 83, 99, 707). The former rest on the principle of identity (or contradiction) or of possibility, in virtue of which that is false which contains a contradiction, and that true which is contradictory to the false. The latter rest on the principle of sufficient reason or of reality (cumpossibilité), according to which no fact is true unless there be a sufficient reason why it should be so and not otherwise (agreeing thus with the p/iiicipiiim melioris or final cause). God alone, the purely active monad, has an a priori knowledge of the latter class of truths; they have their source in the human mind only in so far as it mirrors the outer world, i.e. in its passivity, whereas the truths of reason have their source in our mind in itself or in its activity.

Both kinds of truths fall into two classes, primitive and derivative. The primitive truths of fact are, as Descartes held, those of internal experience, and the derivative truths are inferred from them in accordance with the principle of sufficient reason, by their agreement with our perception of the world as a whole. They are thus reached by probable arguments-a department of logic which Leibnitz was the first to bring into prominence (pp. 84, 164, 168, 169, 343). The primitive truths of reasoning are identical (in later terminology, analytical) propositions, the derivative truths being deduced from them by the principle of contradiction. The part of his logic on which Leibnitz laid the greatest stress was the separation of these rational cognition's into their simplest elements-for he held that the root-notions (cogitation es primae) would be found to be few in number (pp. 92, 93)-and the designation of them by universal characters or symbols,[17] composite notions being denoted by the formulae formed by the union of several definite characters, and judgments by the relation of aequipollence among these formulae, so as to reduce the syllogism to a calculus. This is the main idea of Leibnitz's “ universal characteristic, ” never fully worked out by him, which he regarded as one of the greatest discoveries of the age. An incidental result of its adoption would be the introduction of a universal symbolism of thought comparable to the symbolism of mathematics and intelligible in all languages (cf. p. 356). But the great revolution it would effect would chiefly consist in this, that truth and falsehood would be no longer matters of opinion but of correctness or error in calculation,[18] (pp. 83, 84, 89, 93). The old Aristotelian analytic is not to be superseded; but it is to be supplemented by this new method, for of itself it is but the ABC of logic.

But the logic of Leibnitz is an art of discovery (p. 85) as well as of proof, and, as such, applies both to the sphere of reasoning and to that of fact, In the former it has by attention to render explicit what is otherwise only implicit, and by the intellect to introduce order into the a priori truths of reason, so that one may follow from another and they may constitute together a monde intellectual. To this art of orderly combination Leibnitz attached the greatest importance, and to it one of his earliest writings was devoted. Similarly, in the sphere of experience, it is the business of the art of discovery to find out and classify the primitive facts or data, referring every other fact to them as its sufficient reason, so that new truths of experience may be brought to light.

As the perception of the monad when clarified becomes thought, so the appetite of which all monads partake is raised to will, their spontaneity to freedom, in man (p. 669). The will is an effort or tendency to that which one finds good (p. 251), and is free only in the sense of being exempt from external control[19] (pp. 262, 513, 521), for it must always have a sufficient reason for its action determined by what seems good to it. The end determining the will is pleasure (p: 269), and pleasure is the sense of an increase of perfection (p. 670). A will guided by reason will sacrifice transitory and pursue constant pleasures or happiness, and in this weighing of pleasures consists true wisdom. Leibnitz, like Spinoza, says that freedom consists in following reason, servitude in following the passions (p. 669), and that the passions proceed from confused perceptions (pp. 188, 269). In love one finds joy in the happiness of another; and from love follow justice and law. “Our reason,” says Leibnitz,[20] “illumined by the spirit of God, reveals the law of nature," and with it positive law must not conflict. Natural law rises from the strict command to avoid offence, through the maxim of equity which gives to each his due, to that of probity or piety (honeste vixere), the highest ethical perfection, -which presupposes a belief in God, providence and a future life.</ref>Ibid. IV. iii. 295. Cf. Bluntschli, Gesch. d. allg. Slaatsrechts u. Politik (1864), pp. 143 sqq. Moral immortality—not merely the simple continuity which belongs to every monad-comes from God having provided that the changes of matter will not make man lose his individuality (pp. 126, 466).

Leibnitz thus makes the existence of God a postulate of morality as well as necessary for the realization of the monads. It is in the Théodicée that his theology is worked out and his view of the universe as the best possible world defended. In it he contends that faith and reason are essentially harmonious (pp. 402, 479), and that nothing can be received as an article of faith which contradicts an eternal truth, though the ordinary physical order may be superseded by a higher.[21]

The ordinary arguments for the being of God are retained by Leibnitz in a modified form (p. 375). Descartes's ontological proof is supplemented by the clause that God as the ens a se must either exist or be impossible (pp. 80, 177, 708); in the cosmological proof he passes from the infinite series of finite causes to their sufficient reason which contains all changes in the series necessarily in itself (pp. 147, 708); and he argues teleologically from the existence of harmony among the monads without any mutual influence to God as the author of this harmony (p. 430).

In these proofs Leibnitz seems to have in view an extra mundane power to whom the monads owe their reality, though such a conception evidently breaks the continuity and harmony of his system, and can only be externally connected with it. But he also speaks in one place at any rate[22] of God as the “ universal harmony ”; and the historians Erdmann and Zeller are of opinion that this is the only sense in which his system can be consistently theistic. Yet it would seem that to assume a purely active and therefore perfect monad as the source of all things is in accordance with the principle of continuity and with Leibnitz's conception of the gradation of existences. In this sense he sometimes speaks of God as the first or highest of the monads (p. 678), and of created substances proceeding from Him continually by “ fulgurations ” (p. 708) or by “ a sort of emanation as we produce our thoughts.”[23]

The positive properties or perfections of the monads, Leibnitz holds, exist eminent er, i.e. without the limitation that attaches to created monads (p. 716), in God-their perception as His wisdom or intellect, and their appetite as His absolute will or goodness (p. 654); while the absence of all limitation is the divine independence or power, which again consists in this, that the possibility of things depends on His intellect, their reality on His will (p. 506). The universe in its harmonious order is thus the realization of the divine end, and as such must be the best possible (p. 506). The teleology of Leibnitz becomes necessarily a Théodicée. God created a world to manifest and communicate His perfection (p. 524), and, in choosing this world out of the infinite number that exist in the region of ideas (p. 515), was guided by the principium melioris (p. 506). With this thoroughgoing optimism Leibnitz has to reconcile the existence of evil in the best of all possible worlds.”[24] With this end in view he distinguishes (p. 655) between (1) metaphysical evil or imperfection, which is unconditionally willed by God as essential to created beings; (2) physical evil, such as pain, which is conditionally willed by God as punishment or as a means to greater good (cf. p. 510); and (3) moral evil, in which the great difficulty lies, and which Leibnitz makes various attempts to explain. He says that it was merely permitted not willed by God (p. 655), and, that being obviously no explanation, adds that it was permitted because it was foreseen that the world with evil would nevertheless be better than any other possible world (p. 350). He also speaks of the evil as a mere set-off to the good in the world, which it increases by contrast (p. 149), and at other times reduces moral to metaphysical evil by giving it a merely negative existence, or says that their evil actions are to be referred to men alone, while it is only the power pf actipn that comes from God, and the power of action is good (p. 658).

The great problem of Leibnitz's Théodicée thus remains unsolved. The suggestion that evil consists in a mere imperfection, like his idea of the monads proceeding from God by a continual emanation, was too bold and too inconsistent with his immediate apologetic aim to be carried out by him. Had he done so his theory would have transcended the independence of the monads with which it started, and found a deeper unity in the world than that resulting from the somewhat arbitrary assertion that the monads refiect the universe.

The philosophy of Leibnitz, in the more systematic and abstract form it received at the hands of Wolf, ruled the schools of Germany for nearly a century, and largely determined the character of the critical philosophy by which it was superseded. On it Baumgarten laid the foundations of a science of aesthetic. Its treatment of theological questions heralded the German Aufkldrung. And on many special points-in its physical doctrine of the conservation of force, its psychological hypothesis of unconscious perception, its attempt at a logical symbolism-it has suggested ideas fruitful for the progress of science.

Bibliography.—(1) Editions: Up to 1900 no attempt had been made to publish the complete works. Several editions existed, but a vast mass of MSS. (letters, &c.) remained only roughly classified in the Hanover library. The chief editions were: (1) L. Dutens (Geneva, 1768), called Opera Omnia, but far from complete; (2) G. H. Pertz, Leibrzizens gesammelte Werke (Berlin, 1843-1863) (1st ser. History, 4 vols.; 2nd ser. Philosophy, vol. i. correspondence with Arnauld, &c., ed. C. L. Grotefend; 3rd ser. Mathematics, 7 vols., ed. C. J. Gerhardt); (3) Foucher de Careil (planned in 20 vols., 7 published, Paris, 1859-1875), the same editor having previously published Lehfres et opuscules inédits de Leibniz (Paris, 1854-1857); (4) Onno Klopp, Die Werke von Leibrziz gemdss seirzem Handschriftlichen Nachlasse in der Korziglichen Bibliothek zu Hannover (1st series, Historico-Political and Political, IO vols., 1864-1877). The Œuvres de Leibnitz, by A. Jacques (2 vols., Paris, 1846) also

deserves mention. The philosophical writings had been published by Raspe (Amsterdam and Leipzig, 1765), by J. E. Erdmann, Leibnitii opera philos. quae extant Latina, Gallica, Germanica, omnia (Berlin, 1840), by P. janet (2 vols., Paris, 1866, 2nd ed. 1900), and the fullest by C. J. Gerhardt, Die Philosoplzischen Schriften von G. W. Leibni: (7 vols., 1875~1890); cf. also Die kleineren philos. wichtigeren Schrzften (trans. with commentary, J. H. vonKirchmann, 1879). The German works had also been partly published separately; G. E. Guhrauer (Berlin, 1838-1840). Of the letters various collections had been published up to 1900, e.g.: C. J. Gerhardt (Halle, 1860) and Der Briefwechsel von G. W. Leibnitz mit Mathematikern (1899); Corrispondenza tra L. A. Moratori e G. Leibnitz.. (1899); and cf. Neue Beitrzige zum Briefwechsel zwischen D. E. Jablonsky und G. W. Leibnitz (1899).

In 1900 it was decided by scholars in Berlin and Paris that a really complete edition should be published, and with this object four German and four French critics were entrusted with the preliminary task of correlating the MSS. in the royal library at Hanover. This process resulted in the preparation of the Kritischer Katalog der Leibnitz-Handschriften zur Vorbereitung der interakademischen Leibnitz-Ausgabe unternommen (1908), and also in certain other preliminary publications, e.g. L. Couturat, Operscules et fragments inédits (1903); E. Gerland, Leibnizens nachgelassene Schriften physikalischen, mechanischen und technischen Inhalts (1906); Jean Baruzi, Leibniz (1909), containing unedited MSS. and a sketch biography; cf. the same author's Leibniz et Vorganisation religieuse de lit terre (1907).

Translations.—Of the Systema Theologicum (1850, C. W. Russell), of the correspondence with Clarke (1717); Works, by G. M. Duncan (New Haven, 1890); of the Nouoeaux Essais, by A. G. Langley (London, 1894); the Monadology and other Writings, by R. Latta (Oxford, 1898).

Biographical.—The materials for the life of Leibnitz, in addition to his own works, are the notes of Eckhart (not published till 1779), the Eloge by Fontenelle (read to the French Academy in 1717), the “Eulogium," by Wolf, in the Acta Eruditorium for July 1717, and the "Supplementum" to the same by Feller, published in his Otium Hannoveranum (Leipzig, 1718). The best biography is that of G. E. Guhrauer, G. W. Freiherr von Leibnitz (2 vols., Breslau, 1842; Nachtrage, Breslau, 1846). A shorter Life of G. W. von Leibnitz, on the Basis of the German work of Gutzraner, has been published by J. M. Mackie (Boston, 1845). More recent works are those of L. Grote, Leibniz und seine Zeit (Hanover, 1869); E. Pfieiderer, Leibniz als Patriot, Staatsmann, unzl Bildungstrager (Leipzig, 1870); the slighter volume of F. Kirchner, G. W. Leibniz: sein Leben und Denken (Köthen, 1876); Kuno Fischer, vol. iii. in Gesch. der neuern Philosophie (4th ed., 1902).

Critical.—The monographs and essays on Leibnitz are too numerous to mention, but reference may be made to Feuerbach, Darstellung, Entwicklung, und Kritik der Leibnitz'schen Phil. (2nd ed., Leipzig, 1844); Nourri sson, La Philosophie de Leibniz (Paris, 1860); R. Zimmermann, Leibnitz und Herbart: eine Vergleichung ihrer Monadologieen (Vienna, 1849); O. Caspari, Leibniz' Philosophie beleuehtet vom Gesichtspnnkt der physikalischen Grundbegrije von Kraft und Stojf (Leipzig, 1870); G. Hartenstein, “Lockels Lehre von der menschl. lark. in Vergl. mit Leibniz's Kritik derselben dargestellt," in the Abhandl. d. philol.-hist. Cl. d. K. Sachs. Gesells. d. Wiss., vol. iv. (Leipzig, 1865); G. Class, Die metaph. Voraussetznngen des Ixibnitzisehen Deterrninismus (Tubingen, 1874); F. B. Kvet, Leibnitzens Logik (Prague, 1857); the essays on Leibnitz in Trendelenburg's Beitrfige, vols. ii. and iii. (Berlin, 1855, 1867); L. Neff, Leibniz als Sprachforscher (Heidelberg, 1870-1871); J. Schmidt, Leibniz und Bazimgarten (Halle, 1375); D. Nolen, La Critique de Kant et la Métaphysique de Leibniz (Paris, 1875); and the exhaustive work of -. Pichler, Die Theologie des Leibniz (Munich, 1869-1870). Among the more recent works are: C. Braig, Leibniz: sein Leben und die Bedeutung seiner Lehre (1907); E. Cassirer, Leibniz' System in seinem wissenschaftlichen Griindlagen (1902); L. Couturat, La Logique de Leibniz d'apres des documents inédits (1901); L. Davillé, Leibniz hixtorien (1909); Kuno Fischer, G. W. Leibniz (1889); R. B. Frenzel, Der Associationsbegrij bei Leibniz (1898); R. Herbertz, Die Lehre vom Unbewussten im System des Leibniz (1905); H. Hoffmann, Die Leibnizlrche Religions-philosophies in ihrer geschichtlichen Stellung (1903); W. Kabitz, Die Philosophie des jungen Leibniz (1909), a study of the development of the Leibnitzian system; H. L. Koch, Materie und Organismus bei Leibniz (1908); G. Niel, L'Optimisme de Leibniz (1888); Bertrand A. W. Russell, A Critical Exposition of the Philosophy of Leibniz (1900); F. Schmoger, Leibniz in seiner Stellung zur tellurischen Physik (1901); A. Silberstein, Leibnizens Apriorismus in Verhdltnis zu seiner Metaphysik (1904); Stein, Leibniz uncl Spinoza (1890); F. Thilly, Leibnizens Streit gegen Locke in Ansehung der angeborenen Ideen (1891); R. Urbach, Leibnizens Rechlfertigung des Uebels in der besten Welt (1901); W. Werckmeister, Der Leibnizsche Substanzbegrif (1899); F. G. F. Wernicke, Leibniz' Lehre von der Freiheit des mensch lichen Willens (1890).

  1. Bedenken, welchergestalt securitas pubtica interna et externa und status praesens jetzigen Umstfinden narh im Reich auf festen Fuss zu stelten.
  2. De expeditions Aegyptiatca regi Fmnciae proponenda justa dissertatio.
  3. Consilium Aegyptiacum.
  4. A Summary Account of Leibnitz's Meitzoir addressed to Lewis the Fourteenth, &c. [edited by Granville Penn], (London, 1803).
  5. In a letter to the duke of Brunswick-Lüneburg (autumn 1671), Werke, ed. Klopp, iii. 253 sq.
  6. He was made a foreign member of the French Academy in 1700.
  7. Caesorini Furstenerii lrantotus de jure suprematus ac legatzoms principum Germaniae (Amsterdam, 1677); Entretiens de Philarkfe et d'Eugéue sur Ie droit dlzmbassclde (Duish., 1677).
  8. Not published till 1819. It is on this work that the assertion has been founded that Leibnitz was at heart a Catholic-a supposition clearly disproved by his correspondence.
  9. In his Prologaea (1691) he developed the notion of the historical genesis of the present condition of the earth's surface. Cf. O. Peschel, Gesch. d. Erdkunde (Munich, 1865), pp. 615 sq.
  10. Codex juris geniium diplomulicus (1693); Mtznlissa codicis juri genfium diplamalici (1700).
  11. Memoirs of John Ker of Kersland. by himself (1726), i. 118.
  12. When not otherwise stated, the references are to Erd1nann's edition of the Opera philosophic.
  13. See Considérafions sur la doctrine d'un esprit imizierffel (1702).
  14. Cf. Opera, ed. Dutens, ll. ii. 20.
  15. The difference between an organic and an inorganic body consists, he says, in this, that the former is a machine even in its smallest parts.
  16. Opera. ed. Dutcns, iii. 321.
  17. Different symbolic systems were proposed by Leibnitz at different periods; cf. Kvet, Leibnitzens Logik (1857), p. 37.
  18. The places at which Leibnitz anticipated the modern theory of logic mainly due to Boole are pointed out in Mr Venn's Symbolic Logic (1881).
  19. Hence the difference of his determinism from that of Spinoza, though Leibnitz too says in one place that “it is difficult enough to distinguish the actions of God from those of the creatures" (Werke, ed. Pertz, 2nd ser. vol. i. p. 160).
  20. Opera omnia, ed. Dutens, IV. iii. 282.
  21. P. 480; cf. Werke. ed. Pertz. 2nd ser. vol. i. pp. 158, 159.
  22. Werke, ed. Klopp, iii. 259; cf. Op. phil., p. 716.
  23. Werke, ed. Pertz, 2nd ser. vol. i. p. 167.
  24. "Si c'est ici le meilleur des mondes possibles, que sont donc les autres?”-Voltaire, Candide, ch. vi.